Copyright (c) 2013 John L. Jerz

Liebig's law of the minimum
A Proposed Heuristic for a Computer Chess Program (John L. Jerz)
Problem Solving and the Gathering of Diagnostic Information (John L. Jerz)
A Concept of Strategy (John L. Jerz)
Books/Articles I am Reading
Quotes from References of Interest
Satire/ Play
Viva La Vida
Quotes on Thinking
Quotes on Planning
Quotes on Strategy
Quotes Concerning Problem Solving
Computer Chess
Chess Analysis
Early Computers/ New Computers
Problem Solving/ Creativity
Game Theory
Favorite Links
About Me
Additional Notes
The Case for Using Probabilistic Knowledge in a Computer Chess Program (John L. Jerz)
Resilience in Man and Machine

Perhaps Goldratt's Theory of Constraints had its source in Liebig's law of the minimum

Liebig's Law of the Minimum, often simply called Liebig's Law or the Law of the Minimum, is a principle developed in agricultural science by Carl Sprengel (1828) and later popularized by Justus von Liebig. It states that growth is controlled not by the total of resources available, but by the scarcest resource (limiting factor). This concept was originally applied to plant or crop growth, where it was found that increasing the amount of plentiful nutrients did not increase plant growth. Only by increasing the amount of the limiting nutrient (the one most scarce in relation to "need") was the growth of a plant or crop improved.

Liebig used the image of a barrel—now called Liebig's barrel—to explain his law. Just as the capacity of a barrel with staves of unequal length is limited by the shortest stave, so a plant's growth is limited by the nutrient in shortest supply.

Liebig's Law has been extended to biological populations (and is commonly used in ecosystem models). For example, the growth of an organism such as a plant may be dependent on a number of different factors, such as sunlight or mineral nutrients (e.g. nitrate or phosphate). The availability of these may vary, such that at any given time one is more limiting than the others. Liebig's Law states that growth only occurs at the rate permitted by the most limiting. For instance, in the equation below, the growth of population O is a function of the minimum of three Michaelis-Menten terms representing limitation by factors I, N and P.

 \frac{dO}{dt} = min \left( \frac{I}{k_{I} + I}, \frac{N}{k_{N} + N}, \frac{P}{k_{P} + P} \right)

It is limited to a situation where there are steady state conditions, and factor interactions are tightly controlled.

Enter supporting content here